pacman::p_load(sf, sfdep, tmap, plotly, tidyverse,st,lubridate,arrow,spNetwork,classInt,viridis,raster,spatstat,dplyr,spdep)Take home assignment 3 - Glenn
1.0 Introduction
Singapore, a hallmark of development and urban planning, is renowned for its efficient public transportation system and well-planned residential areas. Despite these achievements, there are recurring concerns among its citizens about the varying levels of convenience and accessibility in different regions. This disparity has led to unequal demand for housing, with some areas being more sought after than others. This project aims to investigate the truth behind these claims, focusing on whether certain areas in Singapore indeed suffer from a lack of accessibility and convenience. By identifying these areas, we intend to highlight potential regions that could benefit from urban planning improvements, thereby enhancing the quality of life for its residents.
1.1 Assigned approach
Hotspot Analysis
- With the accessibility scores calculated for each region, we will perform hotspot analysis to identify areas with significantly higher or lower accessibility levels.
2.0 Goal
The goal of my analysis is to identify areas with higher or lower accessibility levels. I will first import the datasets of each amenities and find the frequency of them per region. Next, i will combine all of them together for an overall view (sum) of amenities for each area.
After that, i will proceed to do Local and Global spatial correlation analysis to identify patterns in the dataset. This will alllow us to find out if there are correlations between areas in Singapore and also allow us to find out if there are clusters that form, indicating a cluster of amenities.
From here, we can also derive areas which needs more / less development and to suggest different regions that we can improve by delegating resources appropriately.
3.0 Getting the data into our R environment
3.1 Importing the packages
3.2 Geospatial data wrangling
mpsz <- st_read(dsn = "data/geospatial",
layer = "MPSZ-2019")Reading layer `MPSZ-2019' from data source
`C:\FieryCake\IS415-GAA\take_home_Ex\take_home_Ex_03\data\geospatial'
using driver `ESRI Shapefile'
Simple feature collection with 332 features and 6 fields
Geometry type: MULTIPOLYGON
Dimension: XY
Bounding box: xmin: 103.6057 ymin: 1.158699 xmax: 104.0885 ymax: 1.470775
Geodetic CRS: WGS 843.2.1 Changing CRS to 3414
mpsz_sf<-st_transform(mpsz,
crs = 3414)3.2.2 Checking if Geometries are valid
length(which(st_is_valid(mpsz_sf) == FALSE))[1] 6From here, we can see that 6 geometries are invalid. We can use the st_make_valid() function to make it valid.
mpsz_sf <- st_make_valid(mpsz_sf)
length(which(st_is_valid(mpsz_sf) == FALSE))[1] 0## source: https://r-spatial.github.io/sf/reference/valid.html - make_valid3.2.3 Removing outer islands
Similarly to take home assignment 1, we do not want to include the outer islands in our analysis.
##source - https://stackoverflow.com/questions/42512431/how-to-separate-a-multipolygon-geometry-into-several-polygons-objects-after-perf
temp <-st_union(mpsz_sf,by_feature = FALSE)
ind_poly <- st_cast(temp, "POLYGON")
sf_use_s2(FALSE)
areas <- st_area(ind_poly)
largest_index <- which.max(areas)
largest_polygon <- ind_poly[largest_index]
plot(largest_polygon)
bigIsland3414 <- st_transform(largest_polygon,
crs = 3414)
st_crs(bigIsland3414)Coordinate Reference System:
User input: EPSG:3414
wkt:
PROJCRS["SVY21 / Singapore TM",
BASEGEOGCRS["SVY21",
DATUM["SVY21",
ELLIPSOID["WGS 84",6378137,298.257223563,
LENGTHUNIT["metre",1]]],
PRIMEM["Greenwich",0,
ANGLEUNIT["degree",0.0174532925199433]],
ID["EPSG",4757]],
CONVERSION["Singapore Transverse Mercator",
METHOD["Transverse Mercator",
ID["EPSG",9807]],
PARAMETER["Latitude of natural origin",1.36666666666667,
ANGLEUNIT["degree",0.0174532925199433],
ID["EPSG",8801]],
PARAMETER["Longitude of natural origin",103.833333333333,
ANGLEUNIT["degree",0.0174532925199433],
ID["EPSG",8802]],
PARAMETER["Scale factor at natural origin",1,
SCALEUNIT["unity",1],
ID["EPSG",8805]],
PARAMETER["False easting",28001.642,
LENGTHUNIT["metre",1],
ID["EPSG",8806]],
PARAMETER["False northing",38744.572,
LENGTHUNIT["metre",1],
ID["EPSG",8807]]],
CS[Cartesian,2],
AXIS["northing (N)",north,
ORDER[1],
LENGTHUNIT["metre",1]],
AXIS["easting (E)",east,
ORDER[2],
LENGTHUNIT["metre",1]],
USAGE[
SCOPE["Cadastre, engineering survey, topographic mapping."],
AREA["Singapore - onshore and offshore."],
BBOX[1.13,103.59,1.47,104.07]],
ID["EPSG",3414]]islandPoly <- st_intersection(st_set_crs(mpsz_sf, 3414),st_set_crs(bigIsland3414, 3414))plot(islandPoly)
mainMap_sf<-st_set_crs(islandPoly, 3414)
st_crs(mainMap_sf)Coordinate Reference System:
User input: EPSG:3414
wkt:
PROJCRS["SVY21 / Singapore TM",
BASEGEOGCRS["SVY21",
DATUM["SVY21",
ELLIPSOID["WGS 84",6378137,298.257223563,
LENGTHUNIT["metre",1]]],
PRIMEM["Greenwich",0,
ANGLEUNIT["degree",0.0174532925199433]],
ID["EPSG",4757]],
CONVERSION["Singapore Transverse Mercator",
METHOD["Transverse Mercator",
ID["EPSG",9807]],
PARAMETER["Latitude of natural origin",1.36666666666667,
ANGLEUNIT["degree",0.0174532925199433],
ID["EPSG",8801]],
PARAMETER["Longitude of natural origin",103.833333333333,
ANGLEUNIT["degree",0.0174532925199433],
ID["EPSG",8802]],
PARAMETER["Scale factor at natural origin",1,
SCALEUNIT["unity",1],
ID["EPSG",8805]],
PARAMETER["False easting",28001.642,
LENGTHUNIT["metre",1],
ID["EPSG",8806]],
PARAMETER["False northing",38744.572,
LENGTHUNIT["metre",1],
ID["EPSG",8807]]],
CS[Cartesian,2],
AXIS["northing (N)",north,
ORDER[1],
LENGTHUNIT["metre",1]],
AXIS["easting (E)",east,
ORDER[2],
LENGTHUNIT["metre",1]],
USAGE[
SCOPE["Cadastre, engineering survey, topographic mapping."],
AREA["Singapore - onshore and offshore."],
BBOX[1.13,103.59,1.47,104.07]],
ID["EPSG",3414]]3.2 Aspatial data wrangling
3.2.1 Importing the data
supermarkets <- read_csv("data/aspatial/supermarket_coordinates.csv")
schools <- read_csv("data/aspatial/school_coordinates.csv")
mrt <- read_csv("data/aspatial/MRT_coordinates.csv")
malls <- read_csv("data/aspatial/mall_coordinates.csv")
hawkers <- read_csv("data/aspatial/hawker_coordinates.csv")3.2.2 Changing coordinates from decimal point degree
supermarkets_sf <- st_as_sf(supermarkets,coords = c("Longitude", "Latitude"),crs = 4326) %>% st_transform(crs = 3414)
schools_sf <- st_as_sf(schools,
coords = c("Longitude", "Latitude"),
crs = 4326) %>%
st_transform(crs = 3414)
mrt_sf <- st_as_sf(schools,
coords = c("Longitude", "Latitude"),
crs = 4326) %>%
st_transform(crs = 3414)
malls_sf <- st_as_sf(malls,
coords = c("Longitude", "Latitude"),
crs = 4326) %>%
st_transform(crs = 3414)
hawkers_sf <- st_as_sf(hawkers,
coords = c("Longitude", "Latitude"),
crs = 4326) %>%
st_transform(crs = 3414)head(supermarkets_sf)Simple feature collection with 6 features and 10 fields
Geometry type: POINT
Dimension: XY
Bounding box: xmin: 34835.39 ymin: 31943.42 xmax: 35988.83 ymax: 32989.44
Projected CRS: SVY21 / Singapore TM
# A tibble: 6 × 11
...1 SEARCHVAL BLK_NO ROAD_NAME BUILDING ADDRESS POSTAL X Y address
<dbl> <chr> <chr> <chr> <chr> <chr> <dbl> <dbl> <dbl> <dbl>
1 0 DBS 112 … 112 EAST COA… DBS 112… 112 EA… 428802 35985. 31943. 428802
2 1 GOLDEN V… 112 EAST COA… GOLDEN … 112 EA… 428802 35989. 31951. 428802
3 2 112 KATO… 112 EAST COA… 112 KAT… 112 EA… 428802 35983. 31949. 428802
4 3 UOB I12 … 112 EAST COA… UOB I12… 112 EA… 428802 35982. 31951. 428802
5 0 KINEX 11 TANJONG … KINEX 11 TAN… 437157 34835. 32989. 437157
6 1 DBS ONE … 11 TANJONG … DBS ONE… 11 TAN… 437157 34835. 32989. 437157
# ℹ 1 more variable: geometry <POINT [m]>3.2.3 Doing changes to the data for later heatmap
3.2.3.1 Finding hawkers and their specific regions
region_supermarkets_intersections <- st_intersection(supermarkets_sf, mainMap_sf) %>%
mutate(area = SUBZONE_C)
region_schools_intersections <- st_intersection(schools_sf, mainMap_sf) %>%
mutate(area = SUBZONE_C)
region_mrt_intersections <- st_intersection(mrt_sf, mainMap_sf) %>%
mutate(area = SUBZONE_C)
region_malls_intersections <- st_intersection(malls_sf, mainMap_sf) %>%
mutate(area = SUBZONE_C)
region_hawkers_intersections <- st_intersection(hawkers_sf, mainMap_sf) %>%
mutate(area = SUBZONE_C)The code above allows us to tag the different amenities to the individual subzones that they belong to.
3.2.3.2 joining data points and the correct subzone
After tagging the specific ameneties with the subzone they belong to, we can do a left join to map to get their specific geometries too. This will be used later on during hotspot analysis for the individual amenities and also all amenities as a whole.
region_supermarkets_intersections2<-st_drop_geometry(region_supermarkets_intersections)
result1 <- left_join(region_supermarkets_intersections2, mainMap_sf, by = c("area" = "SUBZONE_C")) %>% mutate(type = "supermarket")
region_schools_intersections2<-st_drop_geometry(region_schools_intersections)
result2 <- left_join(region_schools_intersections2, mainMap_sf, by = c("area" = "SUBZONE_C"))%>% mutate(type = "school")
region_mrt_intersections2<-st_drop_geometry(region_mrt_intersections)
result3 <- left_join(region_mrt_intersections2, mainMap_sf, by = c("area" = "SUBZONE_C"))%>% mutate(type = "mrt")
region_malls_intersections2<-st_drop_geometry(region_malls_intersections)
result4 <- left_join(region_malls_intersections2, mainMap_sf, by = c("area" = "SUBZONE_C"))%>% mutate(type = "mall")
region_hawkers_intersections2<-st_drop_geometry(region_hawkers_intersections)
result5 <- left_join(region_hawkers_intersections2, mainMap_sf, by = c("area" = "SUBZONE_C"))%>% mutate(type = "hawker")3.2.3.3 selecting type and area only for next step to count frequency
count_result1 <- dplyr::select(result1, type,area)
count_result2 <- dplyr::select(result2, type,area)
count_result3 <- dplyr::select(result3, type,area)
count_result4 <- dplyr::select(result4, type,area)
count_result5 <- dplyr::select(result5, type,area)We then take out the columns that we need which are just the area and type.
3.2.3.4 counting individual ameneties by subzone and then combining them into a df
We then want to find the frequency of each ameneties by region
supermarkets_frequency <- count_result1 %>%
group_by(area) %>%
summarise(frequency = n())
schools_frequency <- count_result2 %>%
group_by(area) %>%
summarise(frequency = n())
mrt_frequency <- count_result3 %>%
group_by(area) %>%
summarise(frequency = n())
malls_frequency <- count_result4 %>%
group_by(area) %>%
summarise(frequency = n())
hawkers_frequency <- count_result5 %>%
group_by(area) %>%
summarise(frequency = n())
combined_frequency <- bind_rows(supermarkets_frequency,schools_frequency,mrt_frequency,malls_frequency,hawkers_frequency)%>% group_by(area) %>%
summarise(frequency = sum(frequency))At the end, we add all the frequencies together and group them by their area. The area code will be used to get the specific gemetry later on
3.2.3.5 Joining to get geometry
combined_frequencyFinal <- left_join(combined_frequency, mainMap_sf, by = c("area" = "SUBZONE_C"))
supermarkets_frequencyFinal <-left_join(supermarkets_frequency, mainMap_sf, by = c("area" = "SUBZONE_C"))
schools_frequencyFinal <-left_join(schools_frequency, mainMap_sf, by = c("area" = "SUBZONE_C"))
mrt_frequencyFinal <-left_join(mrt_frequency, mainMap_sf, by = c("area" = "SUBZONE_C"))
malls_frequencyFinal <-left_join(malls_frequency, mainMap_sf, by = c("area" = "SUBZONE_C"))
hawkers_frequencyFinal <-left_join(hawkers_frequency, mainMap_sf, by = c("area" = "SUBZONE_C"))The above code joins the area and their frequency with the sf object mainMap_sf. This allows each area code to be tagged with the correct geometry.
combined_frequencyFinal <- st_as_sf(combined_frequencyFinal)
supermarkets_frequencyFinal<- st_as_sf(supermarkets_frequencyFinal)
schools_frequencyFinal<- st_as_sf(schools_frequencyFinal)
mrt_frequencyFinal<- st_as_sf(mrt_frequencyFinal)
malls_frequencyFinal<- st_as_sf(malls_frequencyFinal)
hawkers_frequencyFinal<- st_as_sf(hawkers_frequencyFinal)3.3 Plotting the maps
plot(supermarkets_sf)
st_crs(supermarkets_sf)Coordinate Reference System:
User input: EPSG:3414
wkt:
PROJCRS["SVY21 / Singapore TM",
BASEGEOGCRS["SVY21",
DATUM["SVY21",
ELLIPSOID["WGS 84",6378137,298.257223563,
LENGTHUNIT["metre",1]]],
PRIMEM["Greenwich",0,
ANGLEUNIT["degree",0.0174532925199433]],
ID["EPSG",4757]],
CONVERSION["Singapore Transverse Mercator",
METHOD["Transverse Mercator",
ID["EPSG",9807]],
PARAMETER["Latitude of natural origin",1.36666666666667,
ANGLEUNIT["degree",0.0174532925199433],
ID["EPSG",8801]],
PARAMETER["Longitude of natural origin",103.833333333333,
ANGLEUNIT["degree",0.0174532925199433],
ID["EPSG",8802]],
PARAMETER["Scale factor at natural origin",1,
SCALEUNIT["unity",1],
ID["EPSG",8805]],
PARAMETER["False easting",28001.642,
LENGTHUNIT["metre",1],
ID["EPSG",8806]],
PARAMETER["False northing",38744.572,
LENGTHUNIT["metre",1],
ID["EPSG",8807]]],
CS[Cartesian,2],
AXIS["northing (N)",north,
ORDER[1],
LENGTHUNIT["metre",1]],
AXIS["easting (E)",east,
ORDER[2],
LENGTHUNIT["metre",1]],
USAGE[
SCOPE["Cadastre, engineering survey, topographic mapping."],
AREA["Singapore - onshore and offshore."],
BBOX[1.13,103.59,1.47,104.07]],
ID["EPSG",3414]]3.3.1 Plotting supermarkets on the map
tmap_mode("plot")
tm_shape(mainMap_sf) +
tm_polygons() +
tm_shape(supermarkets_sf) +
tm_dots(size = 0.1, col = "red")
3.3.2 Plotting hawkers and supermarkets on the map
tmap_mode("plot")
tm_shape(mainMap_sf) +
tm_polygons() +
tm_shape(hawkers_sf) +
tm_dots(size = 0.5)
tmap_mode("plot")
tm_shape(mainMap_sf) +
tm_polygons() +
tm_shape(supermarkets_sf) +
tm_dots(size = 0.5)
3.3.3 Plotting frequency map (all)
equal <-
tm_shape(islandPoly) +
tm_polygons() +
tm_shape(combined_frequencyFinal) +
tm_fill("frequency",n=4, style = "equal") +
tm_borders(alpha = 0.5)+tm_compass(type="8star",size=2)+tm_scale_bar()+tm_grid(alpha=0.2) +
tm_layout(main.title = "Town Frequency")
quantile<-
tm_shape(islandPoly) +
tm_polygons() +
tm_shape(combined_frequencyFinal) +
tm_fill("frequency",n=10, style = "quantile") +
tm_borders(alpha = 0.5)+tm_compass(type="8star",size=2)+tm_scale_bar()+tm_grid(alpha=0.2) +
tm_layout(main.title = "Town Frequency")
tmap_arrange(equal,
quantile,
asp=1,
ncol=2)
3.3.3 Plotting frequency map (super markets)
equal <-
tm_shape(islandPoly) +
tm_polygons() +
tm_shape(supermarkets_frequencyFinal) +
tm_fill("frequency",n=4, style = "equal") +
tm_borders(alpha = 0.5)+tm_compass(type="8star",size=2)+tm_scale_bar()+tm_grid(alpha=0.2) +
tm_layout(main.title = "Town Frequency")
quantile<-
tm_shape(islandPoly) +
tm_polygons() +
tm_shape(supermarkets_frequencyFinal) +
tm_fill("frequency",n=8, style = "quantile") +
tm_borders(alpha = 0.5)+tm_compass(type="8star",size=2)+tm_scale_bar()+tm_grid(alpha=0.2) +
tm_layout(main.title = "Town Frequency")
tmap_arrange(equal,
quantile,
asp=1,
ncol=2)
write_rds(islandPoly, "data/rds/mpsz.rds")
write_rds(supermarkets_frequencyFinal, "data/rds/supermarketFrequency.rds")
write_rds(schools_frequencyFinal, "data/rds/schoolsFrequency.rds")
write_rds(mrt_frequencyFinal, "data/rds/mrtFrequency.rds")
write_rds(hawkers_frequencyFinal, "data/rds/hawkerFrequency.rds")
write_rds(malls_frequencyFinal, "data/rds/mallstFrequency.rds")
write_rds(combined_frequencyFinal, "data/rds/combinedFrequency.rds")From here, we can choose either quantile or equal. This could be a descriptiive map for our final project to show the distrubution of ameneties for different subzones.
4. Global measures of Spatial autocorrelation
wm_q<-combined_frequencyFinal %>% mutate(nb=st_contiguity(geometry), wt=st_weights(nb,style="W"),.before=1)
wm_q2<-supermarkets_frequencyFinal %>% mutate(nb=st_contiguity(geometry), wt=st_weights(nb,style="W"),.before=1)
wm_q3<-mrt_frequencyFinal %>% mutate(nb=st_contiguity(geometry), wt=st_weights(nb,style="W", allow_zero = TRUE),.before=1)
wm_q4<-hawkers_frequencyFinal %>% mutate(nb=st_contiguity(geometry), wt=st_weights(nb,style="W",allow_zero = TRUE),.before=1)
wm_q5<-malls_frequencyFinal %>% mutate(nb=st_contiguity(geometry), wt=st_weights(nb,style="W",allow_zero = TRUE),.before=1)
#wm_q6<-combined_frequencyFinal %>% mutate(nb=st_contiguity(geometry), wt=st_weights(nb,style="W"),.before=1)4.1 Morans test
set.seed(1234)
bperm = global_moran_perm(wm_q$frequency, ##com
wm_q$nb,
wm_q$wt,
nsim=99)
set.seed(1234)
bperm2 = global_moran_perm(wm_q2$frequency, ##super
wm_q2$nb,
wm_q2$wt,
nsim=99)bperm
Monte-Carlo simulation of Moran I
data: x
weights: listw
number of simulations + 1: 100
statistic = 0.043208, observed rank = 83, p-value = 0.34
alternative hypothesis: two.sidedbperm2
Monte-Carlo simulation of Moran I
data: x
weights: listw
number of simulations + 1: 100
statistic = -0.066351, observed rank = 13, p-value = 0.26
alternative hypothesis: two.sidedLooking at this result, we can see the the p-value is 0.34, which is more than 0.05. This suggest that there no spatial autocorrelation in the data.
4.1.2 Visualising Monte-carlo moran’s test
hist(bperm$res,
freq=TRUE,
breaks=5,
xlab="Simulated Moran's I")
abline(v=0,
col="red") 
4.1.3 Geary C
gperm = global_c_perm(wm_q$frequency,
wm_q$nb,
wm_q$wt,
nsim=99)gperm
Monte-Carlo simulation of Geary C
data: x
weights: listw
number of simulations + 1: 100
statistic = 1.0134, observed rank = 56, p-value = 0.56
alternative hypothesis: greaterhist(gperm$res, freq=TRUE, breaks=20, xlab="Simulated Geary c")
abline(v=1, col="red") 
Looking at the statistic and p-value, p-value shows 0.57 which is significant, indicating that there is no signs of spatial autocorrelation. Statistic is at 1.0134, which is very close to 1. If statistic is 1, it means spatial randomness, meaning no sign of auto correlation. This means that ultimately, it shows almost no signs of spatial correlation
Summary: No Signs of spatial correlation
5. Local measures of Spatial autocorrelation
5.1 Local moran
localMoran = local_moran(wm_q$frequency,
wm_q$nb,
wm_q$wt,
nsim=99)
localMoran2 = local_moran(wm_q2$frequency,
wm_q2$nb,
wm_q2$wt,
nsim=99)
localMoran3 = local_moran(wm_q3$frequency, ##mrt
wm_q3$nb,
wm_q3$wt,
zero.policy = TRUE,
nsim=99)
localMoran4 = local_moran(wm_q4$frequency, ##hawker
wm_q4$nb,
wm_q4$wt,
zero.policy = TRUE,
nsim=99)
localMoran5 = local_moran(wm_q5$frequency, ##mall
wm_q5$nb,
wm_q5$wt,
zero.policy = TRUE,
nsim=99)localMoranData <- cbind(combined_frequencyFinal, localMoran)
localMoranData2 <- cbind(supermarkets_frequencyFinal, localMoran2)
localMoranData3 <- cbind(mrt_frequencyFinal, localMoran3)
localMoranData4 <- cbind(hawkers_frequencyFinal, localMoran4)
localMoranData5 <- cbind(malls_frequencyFinal, localMoran5)fips <-localMoranData$town
printCoefmat(data.frame(
localMoran,
row.names=localMoranData$town),
check.names=FALSE) ii eii var_ii z_ii p_ii p_ii_sim
[1,] -1.9167e-01 7.9018e-03 6.1486e-02 -8.0483e-01 4.2092e-01 4.8000e-01
[2,] 2.6108e-04 4.1462e-03 6.5381e-03 -4.8048e-02 9.6168e-01 8.4000e-01
[3,] -8.0904e-02 -5.9165e-03 2.2147e-02 -5.0388e-01 6.1434e-01 5.2000e-01
[4,] -1.8811e-01 1.4377e-02 6.1081e-02 -8.1929e-01 4.1262e-01 4.2000e-01
[5,] -2.4014e-02 4.0450e-03 3.5329e-02 -1.4928e-01 8.8133e-01 8.8000e-01
[6,] 1.9737e-02 5.3954e-04 7.1828e-04 7.1631e-01 4.7380e-01 5.2000e-01
[7,] -6.7998e-02 1.4460e-04 1.5621e-01 -1.7241e-01 8.6312e-01 8.2000e-01
[8,] 1.0668e-01 3.2847e-03 3.4737e-02 5.5476e-01 5.7906e-01 7.2000e-01
[9,] -6.4716e-03 -8.4907e-02 2.2270e-01 1.6621e-01 8.6799e-01 9.6000e-01
[10,] 4.4175e-02 2.8767e-03 7.4488e-03 4.7851e-01 6.3229e-01 6.6000e-01
[11,] 3.7619e-01 1.3678e-02 1.8905e-02 2.6365e+00 8.3765e-03 6.0000e-02
[12,] -7.4738e-02 1.5558e-03 7.6673e-04 -2.7553e+00 5.8636e-03 2.0000e-02
[13,] -6.1618e-01 3.9558e-02 1.7729e-02 -4.9248e+00 8.4427e-07 2.0000e-02
[14,] 3.6702e+00 -2.2601e-01 3.3403e+00 2.1318e+00 3.3024e-02 1.2000e-01
[15,] 1.7736e+00 -2.6791e-02 2.5751e-01 3.5479e+00 3.8833e-04 2.0000e-02
[16,] 1.6591e+00 -1.6701e-01 4.0854e-01 2.8570e+00 4.2765e-03 4.0000e-02
[17,] -4.0407e-01 -1.1369e-02 1.0334e-01 -1.2216e+00 2.2187e-01 2.2000e-01
[18,] -3.5860e-01 1.3144e-02 1.4235e-01 -9.8528e-01 3.2449e-01 2.0000e-01
[19,] 7.5637e-02 -1.9742e-02 1.2088e-01 2.7433e-01 7.8383e-01 8.4000e-01
[20,] -4.2220e-01 -1.5298e-02 1.2285e-01 -1.1609e+00 2.4567e-01 1.4000e-01
[21,] -1.2377e-01 1.9832e-02 1.5537e-01 -3.6431e-01 7.1563e-01 6.4000e-01
[22,] 2.7788e-01 1.0764e-02 9.2313e-02 8.7915e-01 3.7932e-01 3.8000e-01
[23,] 2.9850e-01 2.0937e-02 1.3707e-01 7.4970e-01 4.5343e-01 4.8000e-01
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[189,] 3.5905e-01 -6.0334e-02 3.4091e-01 7.1828e-01 4.7258e-01 4.8000e-01
[190,] -6.2067e-02 3.6178e-02 9.4903e-02 -3.1891e-01 7.4979e-01 6.2000e-01
[191,] -6.9071e-01 -7.2191e-02 5.1420e-01 -8.6256e-01 3.8838e-01 2.6000e-01
[192,] -2.2346e-02 -1.9023e-03 1.8458e-04 -1.5047e+00 1.3239e-01 6.0000e-02
[193,] 3.0673e-01 3.8819e-03 2.2185e-01 6.4297e-01 5.2024e-01 5.6000e-01
[194,] -1.0782e+00 -3.6967e-02 1.1886e-01 -3.0202e+00 2.5264e-03 6.0000e-02
[195,] 1.0282e+00 -2.1032e-01 2.6045e+00 7.6745e-01 4.4281e-01 4.4000e-01
[196,] 2.6807e+00 3.9858e-02 5.6886e-01 3.5013e+00 4.6294e-04 4.0000e-02
[197,] 7.5290e-01 -1.5977e-02 1.4682e-02 6.3455e+00 2.2169e-10 2.0000e-02
[198,] -8.7932e-01 -2.0208e-02 6.0580e-02 -3.4905e+00 4.8211e-04 2.0000e-02
[199,] -2.1081e-01 -1.8221e-02 7.5965e-02 -6.9874e-01 4.8472e-01 4.6000e-01
[200,] 2.1582e-01 4.2339e-02 4.8470e-02 7.8796e-01 4.3072e-01 5.4000e-01
[201,] 5.4651e-01 -3.3587e-02 1.2048e-01 1.6712e+00 9.4674e-02 8.0000e-02
[202,] 4.8986e-01 -4.5007e-02 1.6142e-01 1.3313e+00 1.8310e-01 2.2000e-01
[203,] -1.9153e-01 2.1476e-02 5.7322e-02 -8.8970e-01 3.7363e-01 3.4000e-01
[204,] -1.5629e-01 -3.2345e-02 3.3092e-02 -6.8135e-01 4.9565e-01 5.8000e-01
[205,] 4.9763e-03 -7.5538e-03 6.4187e-02 4.9457e-02 9.6055e-01 9.6000e-01
[206,] 3.4542e-01 2.7130e-02 1.6954e-01 7.7303e-01 4.3950e-01 4.2000e-01
[207,] 6.9918e-02 -6.8725e-04 5.7007e-03 9.3513e-01 3.4972e-01 3.4000e-01
[208,] 4.5093e-01 9.3700e-03 1.2468e-01 1.2506e+00 2.1110e-01 1.2000e-01
[209,] 1.3957e-01 -9.1507e-03 1.1793e-01 4.3309e-01 6.6495e-01 7.8000e-01
[210,] 1.1805e-01 3.0659e-02 2.1746e-02 5.9261e-01 5.5344e-01 7.6000e-01
[211,] 3.7417e-01 9.9739e-03 1.1668e-01 1.0662e+00 2.8633e-01 3.4000e-01
[212,] 1.5012e-01 5.8381e-03 2.8432e-02 8.5567e-01 3.9218e-01 4.2000e-01
[213,] -6.6740e-02 -2.1182e-03 2.5090e-03 -1.2901e+00 1.9701e-01 1.8000e-01
[214,] -2.6483e-02 9.3001e-03 1.7726e-01 -8.4992e-02 9.3227e-01 8.0000e-01
[215,] 1.9362e-01 -2.2182e-03 4.6307e-02 9.1008e-01 3.6278e-01 2.4000e-01
[216,] 3.1817e-01 -5.0913e-02 1.3649e-01 9.9900e-01 3.1780e-01 3.2000e-01
[217,] -1.3576e-01 -1.8519e-02 7.9352e-02 -4.1620e-01 6.7727e-01 7.8000e-01
[218,] 4.7320e-02 6.9095e-03 3.1255e-03 7.2283e-01 4.6978e-01 5.4000e-01
[219,] 5.0805e-01 -1.2675e-02 2.5275e-01 1.0358e+00 3.0031e-01 3.0000e-01
[220,] 3.1237e-01 -9.2589e-02 1.2310e+00 3.6499e-01 7.1512e-01 6.6000e-01
[221,] 1.3741e+00 -2.8479e-02 4.1668e-01 2.1728e+00 2.9793e-02 6.0000e-02
[222,] -1.2164e-02 2.0763e-03 5.8892e-04 -5.8679e-01 5.5734e-01 5.2000e-01
[223,] -1.2737e-01 9.0590e-03 1.5252e-02 -1.1047e+00 2.6930e-01 2.0000e-01
[224,] -6.6803e-01 2.1082e-04 1.6777e-01 -1.6315e+00 1.0279e-01 1.8000e-01
[225,] -5.6950e-01 -3.9884e-02 2.3108e-01 -1.1017e+00 2.7057e-01 2.6000e-01
[226,] -4.6518e-02 -1.7235e-03 8.7287e-04 -1.5162e+00 1.2947e-01 2.0000e-01
[227,] 2.9838e-02 2.9722e-02 6.0369e-02 4.7274e-04 9.9962e-01 8.6000e-01
[228,] 1.4132e-01 9.5404e-03 1.1811e-01 3.8346e-01 7.0138e-01 6.8000e-01
[229,] 2.1345e-01 -1.0890e-01 1.3361e-01 8.8186e-01 3.7785e-01 3.2000e-01
[230,] -3.0617e-01 9.6409e-02 5.3190e-02 -1.7456e+00 8.0888e-02 1.0000e-01
[231,] -2.6274e-02 3.2289e-03 1.1365e-03 -8.7515e-01 3.8149e-01 3.8000e-01
[232,] -2.2150e-02 -3.3685e-02 1.7728e-01 2.7396e-02 9.7814e-01 8.4000e-01
p_folded_sim skewness kurtosis mean median pysal
[1,] 2.4000e-01 4.7650e-01 3.9566e-01 2.0000e+00 2.0000e+00 2
[2,] 4.2000e-01 -1.0271e+00 1.1079e+00 1.0000e+00 2.0000e+00 1
[3,] 2.6000e-01 -9.7292e-01 1.5654e+00 3.0000e+00 3.0000e+00 3
[4,] 2.1000e-01 -7.0141e-01 -6.6401e-02 3.0000e+00 3.0000e+00 3
[5,] 4.4000e-01 5.6691e-01 2.0135e-01 2.0000e+00 2.0000e+00 2
[6,] 2.6000e-01 -1.1629e+00 3.9693e+00 1.0000e+00 2.0000e+00 1
[7,] 4.0000e-01 -1.0166e+00 1.9175e+00 1.0000e+00 3.0000e+00 3
[8,] 3.7000e-01 -9.2604e-01 6.7116e-01 1.0000e+00 1.0000e+00 1
[9,] 4.8000e-01 -8.2288e-01 2.1722e-01 1.0000e+00 3.0000e+00 3
[10,] 3.4000e-01 -1.3224e+00 2.9412e+00 1.0000e+00 2.0000e+00 1
[11,] 3.0000e-02 9.5856e-01 1.3359e+00 4.0000e+00 4.0000e+00 4
[12,] 1.0000e-02 -3.9875e-01 -9.0205e-01 3.0000e+00 4.0000e+00 3
[13,] 1.0000e-02 -7.0798e-01 7.7434e-01 3.0000e+00 3.0000e+00 3
[14,] 6.0000e-02 6.8817e-01 1.5275e-01 4.0000e+00 4.0000e+00 4
[15,] 1.0000e-02 4.8920e-01 -5.5485e-01 4.0000e+00 4.0000e+00 4
[16,] 2.0000e-02 9.3689e-01 7.6206e-01 4.0000e+00 4.0000e+00 4
[17,] 1.0000e-01 -1.1315e+00 1.4224e+00 3.0000e+00 3.0000e+00 3
[18,] 1.0000e-01 -1.6720e+00 4.5588e+00 3.0000e+00 3.0000e+00 3
[19,] 4.2000e-01 -8.9279e-01 1.6757e+00 1.0000e+00 1.0000e+00 1
[20,] 7.0000e-02 1.4294e+00 2.6321e+00 2.0000e+00 2.0000e+00 2
[21,] 3.2000e-01 -6.5211e-01 5.5110e-01 3.0000e+00 3.0000e+00 3
[22,] 1.9000e-01 -8.9369e-01 7.4289e-01 1.0000e+00 1.0000e+00 1
[23,] 2.5000e-01 -6.8870e-01 6.9099e-02 1.0000e+00 1.0000e+00 1
[24,] 3.9000e-01 9.4342e-01 7.7195e-01 2.0000e+00 2.0000e+00 2
[25,] 2.0000e-01 7.8981e-01 9.0750e-01 2.0000e+00 2.0000e+00 2
[26,] 3.0000e-01 -5.4608e-01 1.0212e-01 1.0000e+00 1.0000e+00 1
[27,] 4.0000e-02 1.0307e+00 1.5970e+00 2.0000e+00 2.0000e+00 2
[28,] 2.5000e-01 -4.7631e-01 -3.8991e-01 1.0000e+00 1.0000e+00 1
[29,] 2.2000e-01 3.0336e-01 1.1397e-01 2.0000e+00 2.0000e+00 2
[30,] 5.0000e-02 1.0739e+00 8.5773e-01 2.0000e+00 2.0000e+00 2
[31,] 2.5000e-01 -4.8193e-01 4.8348e-01 1.0000e+00 1.0000e+00 1
[32,] 1.9000e-01 -9.8114e-01 2.0299e+00 1.0000e+00 2.0000e+00 1
[33,] 4.2000e-01 -1.3304e-01 -4.9211e-01 1.0000e+00 1.0000e+00 1
[34,] 3.7000e-01 -7.5908e-01 4.8957e-01 1.0000e+00 1.0000e+00 1
[35,] 3.6000e-01 -1.1179e+00 2.5270e+00 1.0000e+00 2.0000e+00 1
[36,] 2.6000e-01 -4.5735e-01 -4.6240e-01 1.0000e+00 1.0000e+00 1
[37,] 1.1000e-01 -6.3557e-01 -1.1756e-01 1.0000e+00 1.0000e+00 1
[38,] 4.1000e-01 -9.4187e-01 2.4528e-01 1.0000e+00 1.0000e+00 1
[39,] 2.3000e-01 -7.2211e-01 9.6390e-01 1.0000e+00 1.0000e+00 1
[40,] 2.8000e-01 -1.1021e+00 1.6734e+00 1.0000e+00 1.0000e+00 1
[41,] 6.0000e-02 -1.0770e+00 1.5684e+00 1.0000e+00 1.0000e+00 1
[42,] 4.7000e-01 -9.6054e-01 1.2337e+00 1.0000e+00 2.0000e+00 1
[43,] 4.1000e-01 1.1590e+00 1.8114e+00 2.0000e+00 2.0000e+00 2
[44,] 4.8000e-01 -4.3180e-01 -1.3521e-02 1.0000e+00 2.0000e+00 1
[45,] 4.9000e-01 -1.1915e+00 2.0014e+00 1.0000e+00 1.0000e+00 1
[46,] 3.4000e-01 1.2675e+00 3.3128e+00 2.0000e+00 2.0000e+00 2
[47,] 1.1000e-01 -5.3109e-01 6.2806e-01 1.0000e+00 1.0000e+00 1
[48,] 2.5000e-01 -1.0207e+00 1.1651e+00 3.0000e+00 3.0000e+00 3
[49,] 4.2000e-01 9.3228e-01 6.3901e-01 2.0000e+00 2.0000e+00 2
[50,] 4.5000e-01 8.7390e-01 4.1724e-01 2.0000e+00 4.0000e+00 4
[51,] 3.5000e-01 8.2099e-01 1.0234e+00 2.0000e+00 2.0000e+00 2
[52,] 1.7000e-01 8.9675e-01 2.1584e-01 2.0000e+00 2.0000e+00 2
[53,] 2.6000e-01 1.6362e+00 5.5415e+00 4.0000e+00 4.0000e+00 4
[54,] 5.0000e-02 -7.0661e-01 8.4735e-01 1.0000e+00 1.0000e+00 1
[55,] 4.6000e-01 9.4749e-01 8.5954e-01 2.0000e+00 2.0000e+00 2
[56,] 2.2000e-01 2.2611e-01 -4.7245e-01 2.0000e+00 2.0000e+00 2
[57,] 9.0000e-02 -2.8373e-01 3.0044e-01 1.0000e+00 1.0000e+00 1
[58,] 5.0000e-02 -3.8717e-01 -4.9078e-01 1.0000e+00 1.0000e+00 1
[59,] 1.0000e-01 -1.8145e+00 6.0965e+00 3.0000e+00 3.0000e+00 3
[60,] 8.0000e-02 1.6156e+00 3.7588e+00 2.0000e+00 2.0000e+00 2
[61,] 4.2000e-01 6.4695e-01 3.4940e-01 2.0000e+00 2.0000e+00 2
[62,] 3.8000e-01 -3.7963e-01 -6.8802e-01 3.0000e+00 4.0000e+00 3
[63,] 1.8000e-01 1.0954e+00 1.7597e+00 4.0000e+00 4.0000e+00 4
[64,] 1.7000e-01 1.2454e+00 1.6150e+00 4.0000e+00 4.0000e+00 4
[65,] 2.9000e-01 5.6659e-01 -1.6353e-01 4.0000e+00 4.0000e+00 4
[66,] 2.7000e-01 6.2725e-01 -5.0913e-02 4.0000e+00 4.0000e+00 4
[67,] 3.5000e-01 -8.6143e-01 1.0137e+00 1.0000e+00 1.0000e+00 1
[68,] 4.2000e-01 -4.7788e-01 1.5706e-01 1.0000e+00 1.0000e+00 1
[69,] 5.0000e-01 -1.7621e-01 -4.4062e-01 1.0000e+00 1.0000e+00 1
[70,] 4.1000e-01 -8.3799e-01 1.6002e+00 1.0000e+00 2.0000e+00 1
[71,] 4.4000e-01 -5.5800e-01 -2.3189e-01 1.0000e+00 3.0000e+00 3
[72,] 2.6000e-01 5.8199e-01 4.2496e-01 2.0000e+00 2.0000e+00 2
[73,] 4.9000e-01 1.3313e+00 2.7844e+00 2.0000e+00 2.0000e+00 2
[74,] 3.6000e-01 -1.2010e+00 1.4788e+00 3.0000e+00 3.0000e+00 3
[75,] 5.0000e-01 -1.4487e+00 3.3010e+00 1.0000e+00 2.0000e+00 1
[76,] 1.6000e-01 5.2526e-01 -3.1096e-02 2.0000e+00 2.0000e+00 2
[77,] 4.0000e-01 1.2271e+00 1.9251e+00 2.0000e+00 2.0000e+00 2
[78,] 1.5000e-01 -5.1707e-01 -1.1216e-01 1.0000e+00 1.0000e+00 1
[79,] 2.7000e-01 -1.3321e+00 2.2877e+00 1.0000e+00 1.0000e+00 1
[80,] 6.0000e-02 -8.8214e-01 7.4466e-01 1.0000e+00 1.0000e+00 1
[81,] 9.0000e-02 -6.4177e-01 7.8564e-02 1.0000e+00 1.0000e+00 1
[82,] 3.0000e-02 -7.0566e-01 -4.9033e-02 1.0000e+00 1.0000e+00 1
[83,] 2.5000e-01 -1.6673e+00 3.8114e+00 3.0000e+00 3.0000e+00 3
[84,] 3.6000e-01 -7.4522e-01 1.7195e-01 3.0000e+00 3.0000e+00 3
[85,] 2.3000e-01 -8.0787e-01 5.5073e-01 3.0000e+00 3.0000e+00 3
[86,] 7.0000e-02 4.0899e-01 -3.2856e-01 4.0000e+00 4.0000e+00 4
[87,] 3.0000e-02 -4.0459e-01 -9.5844e-02 3.0000e+00 4.0000e+00 3
[88,] 3.2000e-01 7.9780e-01 4.1374e-01 2.0000e+00 4.0000e+00 4
[89,] 1.0000e-01 1.3596e-01 -5.0537e-01 4.0000e+00 4.0000e+00 4
[90,] 4.0000e-01 6.7545e-01 2.6448e-01 2.0000e+00 4.0000e+00 4
[91,] 3.5000e-01 -9.9980e-01 8.4779e-01 3.0000e+00 3.0000e+00 3
[92,] 9.0000e-02 -8.2531e-01 1.2713e+00 3.0000e+00 3.0000e+00 3
[93,] 2.8000e-01 5.0625e-01 -2.4446e-01 4.0000e+00 4.0000e+00 4
[94,] 1.5000e-01 1.4012e+00 3.2269e+00 4.0000e+00 4.0000e+00 4
[95,] 8.0000e-02 -7.0785e-01 9.4955e-02 3.0000e+00 3.0000e+00 3
[96,] 4.5000e-01 4.9194e-01 4.3518e-01 2.0000e+00 2.0000e+00 2
[97,] 3.6000e-01 -3.3590e-01 -2.0505e-02 3.0000e+00 3.0000e+00 3
[98,] 1.7000e-01 -1.0562e+00 1.6158e+00 3.0000e+00 3.0000e+00 3
[99,] 1.2000e-01 -6.6304e-01 1.9185e-01 3.0000e+00 3.0000e+00 3
[100,] 4.9000e-01 8.5361e-01 1.2909e+00 2.0000e+00 4.0000e+00 4
[101,] 3.3000e-01 1.5502e+00 4.9053e+00 4.0000e+00 4.0000e+00 4
[102,] 1.8000e-01 9.9035e-01 1.4296e+00 4.0000e+00 4.0000e+00 4
[103,] 3.0000e-01 1.2842e+00 2.0370e+00 2.0000e+00 2.0000e+00 2
[104,] 2.0000e-02 -4.4417e-01 4.7494e-01 3.0000e+00 3.0000e+00 3
[105,] 1.8000e-01 -4.7569e-01 -4.7430e-01 3.0000e+00 3.0000e+00 3
[106,] 4.5000e-01 1.1687e+00 1.9869e+00 2.0000e+00 2.0000e+00 2
[107,] 2.3000e-01 1.1768e+00 2.4842e+00 4.0000e+00 4.0000e+00 4
[108,] 1.5000e-01 -8.3096e-01 8.8873e-01 3.0000e+00 3.0000e+00 3
[109,] 2.7000e-01 4.9514e-01 -4.3018e-02 4.0000e+00 4.0000e+00 4
[110,] 3.1000e-01 9.3233e-01 4.2594e-01 2.0000e+00 2.0000e+00 2
[111,] 2.6000e-01 3.4974e-01 -1.4630e-02 2.0000e+00 2.0000e+00 2
[112,] 4.8000e-01 -8.0022e-01 2.1376e-01 1.0000e+00 3.0000e+00 3
[113,] 2.4000e-01 -1.7776e+00 4.3754e+00 3.0000e+00 3.0000e+00 3
[114,] 1.8000e-01 1.1129e+00 1.2345e+00 4.0000e+00 4.0000e+00 4
[115,] 1.0000e-01 5.1686e-01 -2.9134e-01 2.0000e+00 2.0000e+00 2
[116,] 3.6000e-01 -8.5465e-01 6.4337e-01 3.0000e+00 3.0000e+00 3
[117,] 5.0000e-01 -3.2954e-01 -3.1916e-01 1.0000e+00 1.0000e+00 1
[118,] 4.5000e-01 -9.5659e-01 3.1453e-01 1.0000e+00 3.0000e+00 3
[119,] 1.4000e-01 -2.2315e+00 8.6185e+00 3.0000e+00 3.0000e+00 3
[120,] 1.0000e-02 -6.0846e-01 2.8781e-01 3.0000e+00 3.0000e+00 3
[121,] 3.0000e-02 1.4138e+00 3.0138e+00 4.0000e+00 4.0000e+00 4
[122,] 3.4000e-01 1.1658e+00 1.8153e+00 4.0000e+00 4.0000e+00 4
[123,] 1.0000e-02 9.4578e-01 3.9033e-01 2.0000e+00 2.0000e+00 2
[124,] 5.0000e-01 -6.9668e-01 -2.8710e-01 1.0000e+00 1.0000e+00 1
[125,] 3.1000e-01 -1.3816e+00 1.8829e+00 3.0000e+00 3.0000e+00 3
[126,] 4.8000e-01 -7.3391e-01 9.3797e-02 1.0000e+00 3.0000e+00 3
[127,] 3.3000e-01 7.5471e-01 -5.5353e-02 4.0000e+00 4.0000e+00 4
[128,] 2.8000e-01 6.8086e-01 -1.4070e-01 2.0000e+00 2.0000e+00 2
[129,] 2.0000e-01 1.7079e+00 4.3981e+00 4.0000e+00 4.0000e+00 4
[130,] 2.0000e-01 -8.9434e-01 1.4138e+00 3.0000e+00 3.0000e+00 3
[131,] 3.1000e-01 1.5840e+00 3.4403e+00 2.0000e+00 2.0000e+00 2
[132,] 1.6000e-01 9.5654e-01 8.7499e-01 4.0000e+00 4.0000e+00 4
[133,] 3.0000e-02 -4.9606e-01 -6.9341e-02 1.0000e+00 1.0000e+00 1
[134,] 3.5000e-01 -1.4616e+00 1.9927e+00 1.0000e+00 1.0000e+00 1
[135,] 1.0000e-02 -6.2805e-01 9.5447e-01 1.0000e+00 1.0000e+00 1
[136,] 2.0000e-02 -5.6420e-01 -2.2855e-02 1.0000e+00 1.0000e+00 1
[137,] 7.0000e-02 -1.4643e+00 5.1809e+00 3.0000e+00 3.0000e+00 3
[138,] 4.0000e-01 1.0228e+00 2.2171e+00 4.0000e+00 4.0000e+00 4
[139,] 1.0000e-02 -5.2785e-01 -2.1165e-01 3.0000e+00 4.0000e+00 3
[140,] 7.0000e-02 6.5060e-01 -8.9374e-02 4.0000e+00 4.0000e+00 4
[141,] 1.3000e-01 7.0662e-01 3.2763e-01 4.0000e+00 4.0000e+00 4
[142,] 1.9000e-01 -1.0849e+00 2.7556e+00 3.0000e+00 3.0000e+00 3
[143,] 4.1000e-01 -7.5818e-01 4.8023e-01 1.0000e+00 3.0000e+00 3
[144,] 4.5000e-01 1.0458e+00 7.7817e-01 2.0000e+00 2.0000e+00 2
[145,] 3.0000e-02 1.2264e+00 2.8047e+00 4.0000e+00 4.0000e+00 4
[146,] 9.0000e-02 5.0853e-01 -2.2908e-01 4.0000e+00 4.0000e+00 4
[147,] 4.0000e-02 7.2866e-01 1.8814e-01 4.0000e+00 4.0000e+00 4
[148,] 1.0000e-02 -3.9479e-01 -8.4165e-01 3.0000e+00 3.0000e+00 3
[149,] 4.3000e-01 -5.0427e-01 -1.2126e-01 1.0000e+00 1.0000e+00 1
[150,] 1.0000e-01 4.5705e-01 -3.6108e-01 2.0000e+00 2.0000e+00 2
[151,] 2.8000e-01 -1.0994e+00 1.9644e+00 1.0000e+00 1.0000e+00 1
[152,] 2.4000e-01 -6.8073e-01 5.8545e-01 1.0000e+00 1.0000e+00 1
[153,] 5.0000e-02 7.6580e-01 8.3532e-01 2.0000e+00 2.0000e+00 2
[154,] 2.4000e-01 -7.3258e-01 3.4406e-01 1.0000e+00 1.0000e+00 1
[155,] 4.7000e-01 -1.6999e+00 4.9277e+00 1.0000e+00 1.0000e+00 1
[156,] 1.3000e-01 5.1368e-01 2.0975e-01 2.0000e+00 2.0000e+00 2
[157,] 3.8000e-01 -6.8183e-01 -4.8342e-02 1.0000e+00 1.0000e+00 1
[158,] 4.2000e-01 9.9919e-01 1.7862e+00 2.0000e+00 2.0000e+00 2
[159,] 1.8000e-01 -1.5502e+00 3.1037e+00 3.0000e+00 3.0000e+00 3
[160,] 5.0000e-01 6.8785e-01 3.8372e-01 2.0000e+00 2.0000e+00 2
[161,] 3.5000e-01 -1.0797e+00 2.4542e+00 3.0000e+00 3.0000e+00 3
[162,] 1.6000e-01 -1.3262e+00 2.4353e+00 1.0000e+00 1.0000e+00 1
[163,] 8.0000e-02 -8.1699e-01 1.6357e+00 1.0000e+00 1.0000e+00 1
[164,] 3.3000e-01 -6.1087e-01 -2.1625e-01 1.0000e+00 1.0000e+00 1
[165,] 1.5000e-01 -8.6395e-01 3.7323e-01 1.0000e+00 1.0000e+00 1
[166,] 5.0000e-02 -3.7706e-01 1.6304e-01 1.0000e+00 1.0000e+00 1
[167,] 5.0000e-02 -1.2811e+00 2.3884e+00 1.0000e+00 2.0000e+00 1
[168,] 4.4000e-01 -7.9717e-01 8.4490e-01 1.0000e+00 1.0000e+00 1
[169,] 3.1000e-01 -1.3940e+00 2.2343e+00 1.0000e+00 1.0000e+00 1
[170,] 2.1000e-01 -1.1604e+00 1.9787e+00 3.0000e+00 3.0000e+00 3
[171,] 2.2000e-01 -9.6913e-01 7.2462e-01 3.0000e+00 3.0000e+00 3
[172,] 1.0000e-01 1.6583e+00 4.4749e+00 4.0000e+00 4.0000e+00 4
[173,] 4.2000e-01 1.1985e+00 1.4686e+00 2.0000e+00 2.0000e+00 2
[174,] 4.5000e-01 9.0320e-01 5.2510e-01 2.0000e+00 4.0000e+00 4
[175,] 6.0000e-02 -1.1605e+00 1.8672e+00 3.0000e+00 3.0000e+00 3
[176,] 4.0000e-01 8.9214e-01 6.0074e-01 2.0000e+00 4.0000e+00 4
[177,] 1.2000e-01 4.1217e-01 -3.7006e-01 4.0000e+00 4.0000e+00 4
[178,] 1.1000e-01 1.0365e+00 2.5512e+00 4.0000e+00 4.0000e+00 4
[179,] 7.0000e-02 1.0113e+00 2.4275e+00 4.0000e+00 4.0000e+00 4
[180,] 2.4000e-01 7.0392e-01 -2.4419e-02 4.0000e+00 4.0000e+00 4
[181,] 1.2000e-01 -6.9204e-01 5.4241e-01 3.0000e+00 3.0000e+00 3
[182,] 2.3000e-01 -5.0225e-01 -1.4375e-01 3.0000e+00 3.0000e+00 3
[183,] 2.8000e-01 6.9650e-01 7.2434e-01 4.0000e+00 4.0000e+00 4
[184,] 2.1000e-01 -1.4864e+00 3.7386e+00 3.0000e+00 3.0000e+00 3
[185,] 4.8000e-01 9.2766e-01 1.2624e+00 2.0000e+00 2.0000e+00 2
[186,] 2.4000e-01 -5.6360e-01 -3.7908e-01 3.0000e+00 3.0000e+00 3
[187,] 5.0000e-02 -8.4860e-01 -3.6704e-01 3.0000e+00 3.0000e+00 3
[188,] 3.5000e-01 -9.0629e-01 3.4486e-01 1.0000e+00 1.0000e+00 1
[189,] 2.4000e-01 -1.1364e+00 1.7034e+00 1.0000e+00 1.0000e+00 1
[190,] 3.1000e-01 -1.0969e+00 1.1522e+00 1.0000e+00 3.0000e+00 3
[191,] 1.3000e-01 -1.3863e+00 1.6368e+00 3.0000e+00 3.0000e+00 3
[192,] 3.0000e-02 1.0572e+00 2.5326e+00 2.0000e+00 2.0000e+00 2
[193,] 2.8000e-01 -6.4413e-01 -1.2933e-02 1.0000e+00 1.0000e+00 1
[194,] 3.0000e-02 -9.8739e-01 1.0087e+00 3.0000e+00 3.0000e+00 3
[195,] 2.2000e-01 5.1664e-01 -9.1642e-02 4.0000e+00 4.0000e+00 4
[196,] 2.0000e-02 2.1252e+00 9.1216e+00 4.0000e+00 4.0000e+00 4
[197,] 1.0000e-02 8.6654e-01 1.2541e+00 4.0000e+00 4.0000e+00 4
[198,] 1.0000e-02 -4.8762e-01 -2.3665e-03 3.0000e+00 3.0000e+00 3
[199,] 2.3000e-01 -5.0358e-01 -1.2194e-01 3.0000e+00 3.0000e+00 3
[200,] 2.7000e-01 -5.6781e-01 -2.9483e-01 1.0000e+00 1.0000e+00 1
[201,] 4.0000e-02 -8.5622e-01 1.4951e+00 1.0000e+00 1.0000e+00 1
[202,] 1.1000e-01 -2.3760e-01 -7.0962e-01 1.0000e+00 1.0000e+00 1
[203,] 1.7000e-01 -2.4428e-01 1.7627e-01 3.0000e+00 3.0000e+00 3
[204,] 2.8000e-01 7.6976e-01 5.6459e-01 2.0000e+00 2.0000e+00 2
[205,] 4.8000e-01 -3.9993e-01 -4.4398e-01 1.0000e+00 1.0000e+00 1
[206,] 2.1000e-01 -9.6035e-01 1.7775e+00 1.0000e+00 1.0000e+00 1
[207,] 1.7000e-01 -4.9935e-01 -4.9413e-01 1.0000e+00 2.0000e+00 1
[208,] 6.0000e-02 -9.7232e-01 1.1840e+00 1.0000e+00 1.0000e+00 1
[209,] 3.9000e-01 -7.4131e-01 2.5858e-01 1.0000e+00 1.0000e+00 1
[210,] 3.8000e-01 -7.5605e-01 -8.1037e-02 1.0000e+00 1.0000e+00 1
[211,] 1.7000e-01 -4.8478e-01 1.3761e-02 1.0000e+00 1.0000e+00 1
[212,] 2.2000e-01 -8.9318e-01 1.2776e+00 1.0000e+00 1.0000e+00 1
[213,] 9.0000e-02 5.1808e-01 -1.4492e-02 2.0000e+00 2.0000e+00 2
[214,] 3.9000e-01 -1.1315e+00 2.1962e+00 1.0000e+00 3.0000e+00 3
[215,] 1.3000e-01 -2.0736e+00 7.1527e+00 1.0000e+00 1.0000e+00 1
[216,] 1.6000e-01 -1.0662e+00 2.6372e+00 1.0000e+00 1.0000e+00 1
[217,] 3.8000e-01 9.4363e-01 1.4503e+00 2.0000e+00 2.0000e+00 2
[218,] 2.7000e-01 3.7721e-01 -5.4311e-01 4.0000e+00 4.0000e+00 4
[219,] 1.6000e-01 1.0994e+00 2.2181e+00 4.0000e+00 4.0000e+00 4
[220,] 3.3000e-01 7.1158e-01 4.0417e-01 4.0000e+00 4.0000e+00 4
[221,] 3.0000e-02 6.4921e-01 -1.3689e-01 4.0000e+00 4.0000e+00 4
[222,] 2.6000e-01 -4.7074e-01 3.0964e-01 3.0000e+00 4.0000e+00 3
[223,] 1.0000e-01 9.9955e-01 7.2965e-01 2.0000e+00 2.0000e+00 2
[224,] 9.0000e-02 -8.1368e-01 4.4330e-01 3.0000e+00 3.0000e+00 3
[225,] 1.3000e-01 -8.0092e-01 7.7010e-01 3.0000e+00 3.0000e+00 3
[226,] 1.0000e-01 -3.1606e-01 -2.8402e-01 3.0000e+00 4.0000e+00 3
[227,] 4.3000e-01 7.2844e-01 1.5046e-01 2.0000e+00 4.0000e+00 4
[228,] 3.4000e-01 7.2277e-01 1.9403e-01 4.0000e+00 4.0000e+00 4
[229,] 1.6000e-01 4.0888e-01 -3.4765e-01 4.0000e+00 4.0000e+00 4
[230,] 5.0000e-02 -1.8360e-01 -7.5136e-01 3.0000e+00 3.0000e+00 3
[231,] 1.9000e-01 -9.2229e-01 2.2487e-01 3.0000e+00 4.0000e+00 3
[232,] 4.2000e-01 6.0435e-01 5.8040e-01 2.0000e+00 2.0000e+00 2localMI.map <- tm_shape(localMoranData) +
tm_fill(col = "ii",
style = "pretty",
title = "local moran statistics") +
tm_borders(alpha = 0.5)+tm_compass(type="8star",size=2)+tm_scale_bar()+tm_grid(alpha=0.2)
pvalue.map <- tm_shape(localMoranData) +
tm_fill(col = "p_ii",
breaks=c(-Inf, 0.001, 0.01, 0.05, 0.1, Inf),
palette="-Blues",
title = "local Moran's I p-values") +
tm_borders(alpha = 0.5)+tm_compass(type="8star",size=2)+tm_scale_bar()+tm_grid(alpha=0.2)
tmap_arrange(localMI.map, pvalue.map, asp=1, ncol=2)
localMI.map2 <- tm_shape(localMoranData2) +
tm_fill(col = "ii",
style = "pretty",
title = "local moran statistics") +
tm_borders(alpha = 0.5)+tm_compass(type="8star",size=2)+tm_scale_bar()+tm_grid(alpha=0.2)
pvalue.map2 <- tm_shape(localMoranData2) +
tm_fill(col = "p_ii",
breaks=c(-Inf, 0.001, 0.01, 0.05, 0.1, Inf),
palette="-Blues",
title = "local Moran's I p-values") +
tm_borders(alpha = 0.5)+tm_compass(type="8star",size=2)+tm_scale_bar()+tm_grid(alpha=0.2)
tmap_arrange(localMI.map2, pvalue.map2, asp=1, ncol=2)
write_rds(localMoranData, "data/rds/localMoran.rds")
write_rds(localMoranData2, "data/rds/localMoran2.rds")
write_rds(localMoranData3, "data/rds/localMoran3.rds")
write_rds(localMoranData4, "data/rds/localMoran4.rds")
write_rds(localMoranData5, "data/rds/localMoran5.rds")Looking at the map generated above, we can see the statistic figures of local moran and also the p-values. What we can infer from above is that local moran statistics that indicate -4 to -1 means that there is negative spatial correlation and that those 1 to 4 indicate stronger spatial correlation. However, when referencing to the P values map, we can see that majority of the areas are light blue, indicating a p value of 0.1 or more. This means that spatial correlation in those areas are likely by random chance.
Hot Spot and Cold Spot Area Analysis
Source: https://sfdep.josiahparry.com/articles/understanding-emerging-hotspots.html ## Calculating the local Gi*
getis_nb <- combined_frequencyFinal |>
mutate(
nb = include_self(st_contiguity(geometry)),
wt = st_weights(nb)
)
getis_nb2 <- supermarkets_frequencyFinal |>
mutate(
nb = include_self(st_contiguity(geometry)),
wt = st_weights(nb)
)
getis_nb3 <- mrt_frequencyFinal |>
mutate(
nb = include_self(st_contiguity(geometry)),
wt = st_weights(nb)
)
getis_nb4 <- hawkers_frequencyFinal |>
mutate(
nb = include_self(st_contiguity(geometry)),
wt = st_weights(nb)
)
getis_nb5 <- malls_frequencyFinal |>
mutate(
nb = include_self(st_contiguity(geometry)),
wt = st_weights(nb)
) gistar <- getis_nb |>
transmute(gi_star = local_gstar_perm(frequency, nb, wt, nsim = 199)) |>
tidyr::unnest(gi_star)
gistarSimple feature collection with 232 features and 8 fields
Geometry type: GEOMETRY
Dimension: XY
Bounding box: xmin: 2667.538 ymin: 21448.47 xmax: 50271.73 ymax: 49507.46
Projected CRS: SVY21 / Singapore TM
# A tibble: 232 × 9
gi_star e_gi var_gi p_value p_sim p_folded_sim skewness kurtosis
<dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
1 -0.569 0.00447 0.00000123 -0.798 0.425 0.45 0.225 0.430
2 -0.0704 0.00422 0.00000175 -0.00591 0.995 0.86 0.43 0.705
3 0.394 0.00412 0.00000160 0.569 0.569 0.53 0.27 0.640
4 0.431 0.00382 0.00000139 0.914 0.361 0.35 0.175 0.806
5 0.0491 0.00450 0.00000174 -0.0881 0.930 0.92 0.46 0.284
6 -0.668 0.00425 0.00000249 -0.576 0.565 0.62 0.31 0.878
7 -0.207 0.00372 0.00000206 0.160 0.873 0.75 0.39 0.970
8 -0.676 0.00410 0.00000272 -0.577 0.564 0.58 0.28 1.07
9 -0.394 0.00377 0.00000274 -0.0836 0.933 0.95 0.475 0.571
10 -0.535 0.00434 0.00000240 -0.612 0.541 0.52 0.245 0.930
# ℹ 222 more rows
# ℹ 1 more variable: geometry <POLYGON [m]>gistar2 <- getis_nb2 |>
transmute(gi_star2 = local_gstar_perm(frequency, nb, wt, nsim = 199)) |>
tidyr::unnest(gi_star2)
gistar2Simple feature collection with 182 features and 8 fields
Geometry type: GEOMETRY
Dimension: XY
Bounding box: xmin: 2667.538 ymin: 21448.47 xmax: 50271.73 ymax: 49507.46
Projected CRS: SVY21 / Singapore TM
# A tibble: 182 × 9
gi_star e_gi var_gi p_value p_sim p_folded_sim skewness kurtosis
<dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
1 -1.50 0.00599 0.00000272 -1.87 0.0611 0.01 0.005 0.759
2 -1.08 0.00502 0.00000258 -0.865 0.387 0.42 0.21 0.549
3 -0.541 0.00496 0.00000213 -0.270 0.787 0.88 0.435 0.612
4 -1.10 0.00503 0.00000262 -0.811 0.417 0.46 0.215 0.757
5 -1.38 0.00525 0.00000266 -1.31 0.190 0.14 0.07 0.853
6 -1.12 0.00447 0.00000349 -0.684 0.494 0.62 0.285 1.02
7 -1.36 0.00401 0.00000293 -0.965 0.335 0.3 0.13 0.904
8 -0.496 0.00507 0.00000422 -0.348 0.728 0.87 0.415 1.03
9 3.15 0.00583 0.00000282 3.29 0.000990 0.02 0.01 0.921
10 2.04 0.00533 0.00000318 2.23 0.0256 0.06 0.03 1.02
# ℹ 172 more rows
# ℹ 1 more variable: geometry <POLYGON [m]>gistar3 <- getis_nb3 |>
transmute(gi_star3 = local_gstar_perm(frequency, nb, wt, nsim = 199)) |>
tidyr::unnest(gi_star3)
gistar4 <- getis_nb4 |>
transmute(gi_star4 = local_gstar_perm(frequency, nb, wt, nsim = 199)) |>
tidyr::unnest(gi_star4)
gistar5 <- getis_nb5 |>
transmute(gi_star5 = local_gstar_perm(frequency, nb, wt, nsim = 199)) |>
tidyr::unnest(gi_star5)gistar |>
mutate(cluster = case_when(
p_folded_sim > 0.05 ~ "Not Significant",
p_folded_sim <= 0.05 & gi_star < 0 ~ "Low",
p_folded_sim <= 0.05 & gi_star > 0 ~ "High"
)) |>
ggplot(aes(fill = cluster)) +
geom_sf(lwd = 0.2, color = "black") +
scale_fill_manual(values = c("High" = "red",
"Low" = "Blue",
"Not Significant" = "white")) +
theme_void()
gistar2 |>
mutate(cluster = case_when(
p_folded_sim > 0.05 ~ "Not Significant",
p_folded_sim <= 0.05 & gi_star < 0 ~ "Low",
p_folded_sim <= 0.05 & gi_star > 0 ~ "High"
)) |>
ggplot(aes(fill = cluster)) +
geom_sf(lwd = 0.2, color = "black") +
scale_fill_manual(values = c("High" = "red",
"Low" = "Blue",
"Not Significant" = "white")) +
theme_void()
gistar <- gistar %>%
mutate(cluster = case_when(
p_folded_sim > 0.05 ~ "Not Significant",
p_folded_sim <= 0.05 & gi_star < 0 ~ "Low",
p_folded_sim <= 0.05 & gi_star > 0 ~ "High"
))gistar2 <- gistar2 %>%
mutate(cluster = case_when(
p_folded_sim > 0.05 ~ "Not Significant",
p_folded_sim <= 0.05 & gi_star < 0 ~ "Low",
p_folded_sim <= 0.05 & gi_star > 0 ~ "High"
))
gistar3 <- gistar3 %>%
mutate(cluster = case_when(
p_folded_sim > 0.05 ~ "Not Significant",
p_folded_sim <= 0.05 & gi_star < 0 ~ "Low",
p_folded_sim <= 0.05 & gi_star > 0 ~ "High"
))
gistar4 <- gistar4 %>%
mutate(cluster = case_when(
p_folded_sim > 0.05 ~ "Not Significant",
p_folded_sim <= 0.05 & gi_star < 0 ~ "Low",
p_folded_sim <= 0.05 & gi_star > 0 ~ "High"
))
gistar5 <- gistar5 %>%
mutate(cluster = case_when(
p_folded_sim > 0.05 ~ "Not Significant",
p_folded_sim <= 0.05 & gi_star < 0 ~ "Low",
p_folded_sim <= 0.05 & gi_star > 0 ~ "High"
))temp<-st_join(mainMap_sf, gistar, join = st_intersects)
temp[is.na(temp)] <- "Not Significant"
tmap_mode('view')
tm_shape(temp) +
tm_fill(col = "cluster",id = "SUBZONE_N") +
tm_borders()tmap_mode('plot')temp2 <- st_join(mainMap_sf, gistar, join = st_equals)
temp2[is.na(temp2)] <- "Not Significant"
tmap_mode('view')
tm_shape(temp2) +
tm_fill(col = "cluster",id = "SUBZONE_N") +
tm_borders()tmap_mode('plot')temp3<-st_join(mainMap_sf, gistar2, join = st_intersects)
temp3[is.na(temp3)] <- "Not Significant"
tmap_mode('view')
tm_shape(temp3) +
tm_fill(col = "cluster",id = "SUBZONE_N") +
tm_borders()tmap_mode('plot')temp4 <- st_join(mainMap_sf, gistar2, join = st_equals)
temp4[is.na(temp4)] <- "Not Significant"
tmap_mode('view')
tm_shape(temp4) +
tm_fill(col = "cluster",id = "SUBZONE_N") +
tm_borders()tmap_mode('plot')###mrt
temp5<-st_join(mainMap_sf, gistar3, join = st_intersects)
temp5[is.na(temp5)] <- "Not Significant"
temp6 <- st_join(mainMap_sf, gistar3, join = st_equals)
temp6[is.na(temp6)] <- "Not Significant"
## hawker
temp7<-st_join(mainMap_sf, gistar4, join = st_intersects)
temp7[is.na(temp7)] <- "Not Significant"
temp8 <- st_join(mainMap_sf, gistar4, join = st_equals)
temp8[is.na(temp8)] <- "Not Significant"
##mall
temp9<-st_join(mainMap_sf, gistar5, join = st_intersects)
temp9[is.na(temp9)] <- "Not Significant"
temp10 <- st_join(mainMap_sf, gistar5, join = st_equals)
temp10[is.na(temp10)] <- "Not Significant"write_rds(temp, "data/rds/hotspot.rds")
write_rds(temp2, "data/rds/hotspot2.rds")
write_rds(temp3, "data/rds/hotspot3.rds")
write_rds(temp4, "data/rds/hotspot4.rds")
write_rds(temp5, "data/rds/hotspot5.rds")
write_rds(temp6, "data/rds/hotspot6.rds")
write_rds(temp7, "data/rds/hotspot7.rds")
write_rds(temp8, "data/rds/hotspot8.rds")
write_rds(temp9, "data/rds/hotspot9.rds")
write_rds(temp10, "data/rds/hotspot10.rds")Summary: Looking at the Global correlation results, we can see that we have no spatial correlation in our dataset. However, when looking at local spatial correlation results, we can see that there are some signs of clustering in the east side of Singapore.
There is no patterns when looking at Singapore as a whole but that when looking at regions / subzones in their independant state, we find that there are some relationship / hotspots that came out in the eastern side of Singapore.
UI design
For the UI Design section, we will be referencing the Layout from the Shiny workshop. From there, we will select a Shiny Layout panel we want to use to present our data.
The layouts above are the templates that we have learnt in the workshop. For each graph to present, i will be usinng a layout that will be appealing to users.
Graph 1
For the graph above, the different parameters required for this fields are the following
Frequency of amenities (Combined, hawker, schools etc)
N (Number of bins)
Style (Equal or Quantile)
From here, we can implement a sidebarLayout. The side panel will consist of sliders to allow user to customize the parameters above. The main panel will be used to display the graph as the output.
Graph 2
For the graph above, the different parameters required for this fields are the following
Category of amenities (Combined, hawker, schools etc)
Col (P value, Statistics)
From here, we can implement a sidebarLayout. The side panel will consist of sliders to allow user to customize the parameters above. The main panel will be used to display the graph as the output.
Graph 3
Category of amenities (Combined, hawker, schools etc)
Region
From here, we can implement a sidebarLayout. The side panel will consist of sliders to allow user to customize the parameters above. The main panel will be used to display the graph as the output.
